基于响应面建模和改进粒子群算法的有限元模型修正方法
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摘要
现代飞行器多采用平台化、模块化设计以缩短研制周期,节约研究经费,新型航天器往往采用对成熟平台的改进就能完成设计,以适应空间市场的快速发展。基于MSC/PATRAN的模型修正技术在航空航天领域应用广泛,目前主要根据工程人员经验对可能存在误差的建模部位及结构参数进行多次调整,限制了修正效率和精度。基于响应面的模型修正方法可以避免基于有限元的模型修正过程中结构参数的每次变化都要调用有限元程序计算从而导致效率低下的缺点,且有限元软件不易与新兴的粒子群算法等优化算法结合等缺点。响应面方法和优化算法结合进行模型修正,可以有效确定模型误差所在位置及参数修正值,同时给出各误差参数间定量的对应关系,还可以通过设定多个修正目标的适应度函数使得修正后模型在多种分析计算方面的性能都得到改善。本文主要从以下三个方面进行了研究:
在分析现有粒子群算法运算特点及所存在的缺陷基础上提出了基于分组控制策略的改进粒子群算法,将粒子按适应度分为优解群和劣解群,将优解群中的粒子引入混沌搜索机制,增加粒子多样性;对劣解群中的粒子进行变异,有效帮助其脱离劣解群,增大寻求最优解的概率。分析了改进粒子群算法中粒子飞行轨迹和速度的收敛条件,通过计算得到了使得算法收敛的参数取值范围,为改进算法中各参数的选取提供指导。
响应面模型的构成形式是影响响应面精度的主要因素,通过比较各种形式响应面的构成及计算效果,提出了线性—高斯组合核支持向量机响应面,该响应面综合了一次多项式的线性模拟能力和高斯核的非线性拟合能力,具有良好的计算精度和广泛的适用范围。为表示响应面模型中各参数对计算结果的不同影响程度,引进加权思想,通过分析提出了适用于显式函数的由响应面函数计算各结构参数在各设计点处偏导数作为评价各参数对结构响应影响程度的加权方式和适用于实际工程结构的由分析所得结构参数对响应影响度作评价标准的加权方式,依此构造加权矩阵。加权线性—高斯组合核支持向量机响应面能有效提高分析效率和精度,在选取高斯核中参数σ时,经多次试验发现σ取函数设计空间半径时能取得良好的拟合效果。
详细介绍了基于响应面方法的模型修正过程和基于有限元等方法的模型修正过程的不同,用组合粒子群算法和加权线性—高斯组合核支持向量机响应面对多铺层碳纤维蜂窝板模型进行修正,通过该例给出了基于响应面方法的模型修正的清晰思路和过程,检验了响应面方法修正后的模型在试验频段内的复现能力和试验频段外的预测能力,并对修正前后模型与基准模型的原点和跨点频响函数进行对比,证实了修正模型的有效性。将加权线性—高斯组合核支持向量机响应面和分组控制粒子群算法应用于卫星有限元模型修正,修正后模型计算所得模态频率和频响分析结果均有所改善,证实了该修正方法在工程复杂结构中的适用性。
Platformization and modularization are employed in modern aircraft design to save research grant and shorten lead time, new spacecraft often improve the existing mature platform to meet the design requirement and the rapid expansion of the space market. The MSC/PATRAN-based model updating technology is widely used in aerospace field, and the updating process largely depends on the engineers’experiments to adjust the error location and model parameters, which decreases the updating efficiency and precision. The RSM-based model updating method doesn’t need to call the FEM program in every iteration process following the parameter variation, which reduces the solving efficiency, and this method avoids the disability of FEM-based model updating method that hard to combine with the PSO algorithm. The RSM and PSO-based model updating method can effectively confirm the error location and model parameters, it can also give the quantitative correspondence of each error parameter, and various analysis abilities of the updating model are largely improved by setting multi-objective fitting function.
The group-control-based improved PSO algorithm is proposed based on the analysis of the algorithm mechanism and defect of the existing PSO algorithm, which divides the particle swarm into two groups, that is, the superior group and the inferior group, the chaos search mechanism is introduced into the superior group to increase the diversity and the variation mechanism is introduced into the inferior group to break the inferior particles away from the inferior solution so as to increase the probability of finding the optimum solution. Convergence condition of the flying path and velocity of the particles are analyzed and the parameter range that makes the algorithm converge is derived, which provides guidance for the parameter selection in the improved algorithm.
Model composition is the main influencing factor of the RSM, comparing the composition and calculating effect of each response surface model, the Linear-and-Gaussian combined kernel function support vector machine response surface is proposed which combines the linear fitting ability of the linear polynomial and the nonlinear fitting ability of the Gaussian polynomial with better calculation precision and widely scope of application. The weight thought is introduced into the response surface method in order to show that different parameter has different influence on the calculated result, and the weighted matrix is given by the partial derivative of the response surface to the structure parameters at different design points, which fits the explicit functions, as well as the effectiveness of structure parameters have on responses, which fits the real structures. The weighted least square support vector machine (WLS-SVM) is proposed and the construction and calculation precision are contrasted, The weighted Linear-and-Gaussian can effectively improve the analysis efficiency and precision, set the kernel factorσto be equal to the radius of the design space and then favorable fitting results are obtained.
The differences between the RSM-based model updating method and the FEM-based model updating method are introduced in detail, and the combined PSO algorithm and Linear-and-Gaussian combined kernel function support vector machine response surface are used to update the multi-layered carbon fiber honeycomb sandwich panel, which shows the clear process of RSM-based model updating, the reappearance ability in the updated frequency range and prediction ability out of the updated frequency range of the updated model are tested and the updating validity is verified. Then the Linear-and-Gaussian combined kernel function support vector machine response surface and the group-control PSO algorithm are applied to the satellite model updating, the modal frequency and frequency response analysis results of the updated model are both improved, which verifies the applicability of the updating method.
在分析现有粒子群算法运算特点及所存在的缺陷基础上提出了基于分组控制策略的改进粒子群算法,将粒子按适应度分为优解群和劣解群,将优解群中的粒子引入混沌搜索机制,增加粒子多样性;对劣解群中的粒子进行变异,有效帮助其脱离劣解群,增大寻求最优解的概率。分析了改进粒子群算法中粒子飞行轨迹和速度的收敛条件,通过计算得到了使得算法收敛的参数取值范围,为改进算法中各参数的选取提供指导。
响应面模型的构成形式是影响响应面精度的主要因素,通过比较各种形式响应面的构成及计算效果,提出了线性—高斯组合核支持向量机响应面,该响应面综合了一次多项式的线性模拟能力和高斯核的非线性拟合能力,具有良好的计算精度和广泛的适用范围。为表示响应面模型中各参数对计算结果的不同影响程度,引进加权思想,通过分析提出了适用于显式函数的由响应面函数计算各结构参数在各设计点处偏导数作为评价各参数对结构响应影响程度的加权方式和适用于实际工程结构的由分析所得结构参数对响应影响度作评价标准的加权方式,依此构造加权矩阵。加权线性—高斯组合核支持向量机响应面能有效提高分析效率和精度,在选取高斯核中参数σ时,经多次试验发现σ取函数设计空间半径时能取得良好的拟合效果。
详细介绍了基于响应面方法的模型修正过程和基于有限元等方法的模型修正过程的不同,用组合粒子群算法和加权线性—高斯组合核支持向量机响应面对多铺层碳纤维蜂窝板模型进行修正,通过该例给出了基于响应面方法的模型修正的清晰思路和过程,检验了响应面方法修正后的模型在试验频段内的复现能力和试验频段外的预测能力,并对修正前后模型与基准模型的原点和跨点频响函数进行对比,证实了修正模型的有效性。将加权线性—高斯组合核支持向量机响应面和分组控制粒子群算法应用于卫星有限元模型修正,修正后模型计算所得模态频率和频响分析结果均有所改善,证实了该修正方法在工程复杂结构中的适用性。
Platformization and modularization are employed in modern aircraft design to save research grant and shorten lead time, new spacecraft often improve the existing mature platform to meet the design requirement and the rapid expansion of the space market. The MSC/PATRAN-based model updating technology is widely used in aerospace field, and the updating process largely depends on the engineers’experiments to adjust the error location and model parameters, which decreases the updating efficiency and precision. The RSM-based model updating method doesn’t need to call the FEM program in every iteration process following the parameter variation, which reduces the solving efficiency, and this method avoids the disability of FEM-based model updating method that hard to combine with the PSO algorithm. The RSM and PSO-based model updating method can effectively confirm the error location and model parameters, it can also give the quantitative correspondence of each error parameter, and various analysis abilities of the updating model are largely improved by setting multi-objective fitting function.
The group-control-based improved PSO algorithm is proposed based on the analysis of the algorithm mechanism and defect of the existing PSO algorithm, which divides the particle swarm into two groups, that is, the superior group and the inferior group, the chaos search mechanism is introduced into the superior group to increase the diversity and the variation mechanism is introduced into the inferior group to break the inferior particles away from the inferior solution so as to increase the probability of finding the optimum solution. Convergence condition of the flying path and velocity of the particles are analyzed and the parameter range that makes the algorithm converge is derived, which provides guidance for the parameter selection in the improved algorithm.
Model composition is the main influencing factor of the RSM, comparing the composition and calculating effect of each response surface model, the Linear-and-Gaussian combined kernel function support vector machine response surface is proposed which combines the linear fitting ability of the linear polynomial and the nonlinear fitting ability of the Gaussian polynomial with better calculation precision and widely scope of application. The weight thought is introduced into the response surface method in order to show that different parameter has different influence on the calculated result, and the weighted matrix is given by the partial derivative of the response surface to the structure parameters at different design points, which fits the explicit functions, as well as the effectiveness of structure parameters have on responses, which fits the real structures. The weighted least square support vector machine (WLS-SVM) is proposed and the construction and calculation precision are contrasted, The weighted Linear-and-Gaussian can effectively improve the analysis efficiency and precision, set the kernel factorσto be equal to the radius of the design space and then favorable fitting results are obtained.
The differences between the RSM-based model updating method and the FEM-based model updating method are introduced in detail, and the combined PSO algorithm and Linear-and-Gaussian combined kernel function support vector machine response surface are used to update the multi-layered carbon fiber honeycomb sandwich panel, which shows the clear process of RSM-based model updating, the reappearance ability in the updated frequency range and prediction ability out of the updated frequency range of the updated model are tested and the updating validity is verified. Then the Linear-and-Gaussian combined kernel function support vector machine response surface and the group-control PSO algorithm are applied to the satellite model updating, the modal frequency and frequency response analysis results of the updated model are both improved, which verifies the applicability of the updating method.
引文
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